That's nice, but I can guarantee any software house that only implements provable algorithms will get crushed in the marketplace by a company that uses agile methodologies to produce software that is "good enough" because the agile company will ship first. Ship Or Die.

In a risk-return analysis, test-first design will beat mathematical analysis in all but a few niches.

Also, you can't be competetive in the marketplace if you have to re-prove your code every time you have to adapt your code for a new feature, or refactoring.